Thursday, October 28, 2010
2010 GCE-O Level Additional Mathematics Paper 2
My dearest Sec 4 Express and Sec 5 pupils,
Please focus your attention on the following topics for your revision for Additional Mathematics Paper 2: (Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Tomorrow's paper)
To help you further, I will be using the following colour codes: blue - very likely topic, green - maybe only, red - no need to study le.
VERY LIKELY TOPICS
Please focus your attention on the following topics for your revision for Additional Mathematics Paper 2: (Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Tomorrow's paper)
To help you further, I will be using the following colour codes: blue - very likely topic, green - maybe only, red - no need to study le.
VERY LIKELY TOPICS
1 Algebra
1.1 Quadratic equations and inequalities: (Chapter 2)
• conditions for a quadratic equation to have: (i) two real roots, (ii) two equal roots, (iii) no real roots and related conditions for a given line to: (i) intersect (ii) not intersect or (iii) be a tangent to a given curve
1.2 Indices and surds: (Chapter 4)
• solving equations involving indices and surds
1.5 Partial fractions: (Chapter 3)
• usually together with differentiation or integration
1.6 Binomial expansions: (Chapter 9)
• please practise term independent of x, coefficients, n!
1.7 Exponential and logarithmic functions (Chapter 16)
1.6 Binomial expansions: (Chapter 9)
• please practise term independent of x, coefficients, n!
1.7 Exponential and logarithmic functions (Chapter 16)
• solving simple equations involving exponential, logarithmic
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• sketching, amplitude, period
• R formula
• solution of simple trigonometric equations in a given interval
2.2 Coordinate geometry in two dimensions (Chapter 5)
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices
2.3 Proofs in plane geometry (Chapter 10)
• do not spend too much time here if you are not too confident, use your knowledge in congruency and similarity to gain some marks here (if you are game for this, go to elearn portal for last Saturday’s revision worksheet with worked solutions)
3 Calculus
3.1 Differentiation and integration (Chapters 12 to 18)
• definite integral as area under a curve
• finding the area of a region bounded by a curve and lines parallel to the coordinate axes
• finding areas of regions below the x-axis
• application of differentiation and integration to problems involving displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration (for sure one question on Kinematics)
Next up will be topics that maybe tested too
MAYBE ONLY
1 Algebra
1.4 Simultaneous equations in two unknowns: (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method (revise conditions for no solution / infinite number of solutions)
Next up will be topics that maybe tested too
MAYBE ONLY
1 Algebra
1.4 Simultaneous equations in two unknowns: (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method (revise conditions for no solution / infinite number of solutions)
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• proofs of simple trigonometric identities
2.2 Coordinate geometry in two dimensions (Chapter 11)
• graphs of y = ax^n and y^2 = kx
3 Calculus
3.1 Differentiation and integration
• applying differentiation to gradients, tangents and normals,
Finally, we have come to the topics that you do not have to give any attention to:
NO NEED TO STUDY LE (a few cheers! very loud ones, eh no jeering pls)
1 Algebra
1.1 Quadratic equations and inequalities (chapter 2)
• solution of quadratic inequalities, and the representation of the solution set on the number line
• relationships between the roots and coefficients of the quadratic equation
ax2 + bx + c = 0 (α + β, αβ)
1.3 Polynomials: (Chapter 1)
• use of remainder and factor theorems
1.7 modulus functions (Chapters 2)
• solving simple equations involving modulus functions
• sketching
2 Geometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• exact values of the trigonometric functions for special angles (30°, 45°, 60°)
2.2 Coordinate geometry in two dimensions (Chapters 5, 11)
• transformation of given relationships, including y = axn and y = kbx, to linear form to determine the unknown constants from the straight line graph
• coordinate geometry of the circle, (centre, radius, reflection, conditions for touching axes/lines)
3 Calculus
3.1 Differentiation and integration
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• use of second derivative test to discriminate between maxima and minima
• rate of change (Chapter 14)
• increasing and decreasing functions (Chapter 13)
Hope that this analysis will help you to be more focussed in your revision.
Do your best, let GOD do the rest.
Yours sincerely,
Mr Ng Song Seng
Tuesday, October 26, 2010
GCE-O Level Mathematics Paper 2 (2010)
My dearest Sec 4 Express, Sec 4NA and Sec 5 pupils,
Please focus your attention on the following topics for your revision for Paper 2: (Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Tomorrow's paper)
To help you further, I will be using the following colour codes: blue - very likely topic, green - maybe only, red - no need to study le.
Please focus your attention on the following topics for your revision for Paper 2: (Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Tomorrow's paper)
To help you further, I will be using the following colour codes: blue - very likely topic, green - maybe only, red - no need to study le.
You should study blue colour topic then green. You may want to skip red completely.
Before we jump into the topics, just a reminder to all additional maths pupils: Your Chemistry teachers are concerned that you may focus too much on Maths and neglect Friday’s Chemistry, so please don’t forget to revise a little bit of Chemistry. I will also be putting up solutions to last Saturday’s Geometrical Proof in elearn portal. Please also refer to the elearn portal for a detailed breakdown of number of questions per topic for Additional Maths based on analysis of past year papers.
Let's jump right in.VERY LIKELY TOPICS
Numbers & Algebra
1. Functions and Graphs
• plotting of points & drawing of curves
• estimation of gradients by drawing tangents, finding the point given the gradient (for additional maths pupils, please use differentiation to check your answers)
• add lines or curves to the original graph to solve equations, inequalities
• find equation of curve (for questions in which points are given but equation not given)
2. Problems derived from practical situations
• utilities bills
• hire-purchase
• simple interest and compound interest
• money exchange
• profit and loss
• taxation
3. Formulating equation to solve problem. The type of question that asks you to form an equation and reduced to the form ax^2 + bx + c = 0 then solve using formula.
• taxation
3. Formulating equation to solve problem. The type of question that asks you to form an equation and reduced to the form ax^2 + bx + c = 0 then solve using formula.
4. Algebra: complete square then use it to solve quadratic equation (if don’t have formulating equation to solve problem then this one sure have), factorization by grouping, simultaneous equations, should have no more algebraic fractions
Geometry
Geometry
5. Angles
• parallel lines
• parallel lines
• triangles and special quadrilaterals
• polygons
• circle properties (between green and blue, although already three marks in paper 1)
6. Trigonometry
• sine rule, cosine rule
• pythagoras theorem, toa-cah-soh
• 2- and 3- dimension problems (angle of elevation, depression, shortest distance, largest angle of elevation and depression, bearings)
7. Mensuration
• total surface area and volume of all sorts of solids
• perimeter and area of all sorts of plane figures
6. Trigonometry
• sine rule, cosine rule
• pythagoras theorem, toa-cah-soh
• 2- and 3- dimension problems (angle of elevation, depression, shortest distance, largest angle of elevation and depression, bearings)
7. Mensuration
• total surface area and volume of all sorts of solids
• perimeter and area of all sorts of plane figures
• radian measure (sector, segment, make sure you calculate everything in radians and do not keep converting between degrees and radians)
8. Vectors in two dimensions
• position vectors
• magnitude
• parallel vectors
• triangle law of vectors addition
9. Statistics
• dot diagram, box-and-whisker plots, histogram, cumulative frequency curve or combination of the last three types
• mean and standard deviation
• comparing spread (consistency based on standard deviation)
• comparing performance (based on mean)
Next up are the topics that may also be tested
MAYBE ONLY
Number & Algebra
1. Number Pattern
2. Percentages greater than 100%
9. Statistics
• dot diagram, box-and-whisker plots, histogram, cumulative frequency curve or combination of the last three types
• mean and standard deviation
• comparing spread (consistency based on standard deviation)
• comparing performance (based on mean)
Next up are the topics that may also be tested
MAYBE ONLY
Number & Algebra
1. Number Pattern
2. Percentages greater than 100%
3. Scale and map
Geometry
4. Coordinate Geometry (y = mx + c)
Geometry
4. Coordinate Geometry (y = mx + c)
5. Circle Properties (quite likely)
Statistics
6. Probabilities (because only 3 marks in paper 1)
Finally, the topics that you may choose to give little or no attention to:NO NEED TO STUDY LE
Numbers and Algebra
1. H.C.F. and L.C.M.
2. Very large and very small numbers (Mega, Giga, Nano, Pico, etc)
3. Indices
Statistics
6. Probabilities (because only 3 marks in paper 1)
Finally, the topics that you may choose to give little or no attention to:NO NEED TO STUDY LE
Numbers and Algebra
1. H.C.F. and L.C.M.
2. Very large and very small numbers (Mega, Giga, Nano, Pico, etc)
3. Indices
4. Algebraic fractions
5. Solving inequalities
5. Solving inequalities
6. Proportion
7. Matrices
8. Sketching graphs
9. Distance-time and Speed-time graphs
9. Distance-time and Speed-time graphs
10. Sets (Venn Diagram, union, intersection, empty set, subset)
Geometry
11. Congruence and similarity
Statistics
12. Stem-and-Leaf
Geometry
11. Congruence and similarity
Statistics
12. Stem-and-Leaf
Hope that this analysis will help you to be more focussed in your revision.
Do your best, let GOD do the rest.
Yours sincerely,
Mr Ng Song Seng
Tuesday, October 05, 2010
2010 GCE-N Level Mathematics Paper 2
My dearest 4C and 4D pupils,
Please focus your attention to the following topics:
(Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Thursday's paper)
To help you further, I will be using the following colour codes: blue - very likely topic, red - no need to study already
VERY LIKELY TOPICS
1. Percentages – problems involving percentages
To help you further, I will be using the following colour codes: blue - very likely topic, red - no need to study already
VERY LIKELY TOPICS
1. Percentages – problems involving percentages
2. Applications of Mathematics in practical situations – compound interest, taxation, money exchange, etc.
3. Functions and Graphs – graphs of quadratic functions and their properties, sketching quadratic graphs including maximum/minimum point, line of symmetry, where the graphs cut the x an y axes, AND for sure one big question on drawing graph on graph paper and finding information from the graph for example estimation of gradient of the curve by drawing a tangent, etc.
4. Solutions of equations and inequalities – simultaneous equations, solving inequalities such as 3x < 7, complete square etc and some simple algebra
5. Angles – vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, angles formed by two parallel lines and a transversal: corresponding, alternate and interior angles.
6. Congruence and similarity – solving simple problems involving similarity and congruence.
7. Properties of Circles – angle and symmetry properties of circles
8. Pythagoras’ Theorem and Trigonometry – use of Pythagoras’ Theorem, sine and cosine rules, bearings, angle of elevation/depression, area of triangle = half a b sin C
9. Mensuration – volume and total surface area, radian measure: use of radian measure of angle, length of arc, area of sector, area of segment
10. Coordinate Geometry – finding gradient/equation of a straight line given two points, y = mx + c. (No need to learn distance between two points)
11. Statistics – range, interquartile range, standard deviation, mode and median, cumulative frequency, box-and-whisker plots, stem-and-leaf, dot diagram, histogram
12. Probability of simple combined events (using possibility diagrams, tree diagrams)
NO NEED TO STUDY
1. Prime factorization - H.C.F. / L.C.M.
2. Standard form – Mega, Giga, Terra, micro, nano, pico
3. Ratio, Rate and Proportion – y = kx where k is a constant
4. Distance/Speed/Time
5. Algebraic fractions
6. Scale drawings, scale and maps
7. Angle Properties of Polygons
8. Pie Chart
9. ConstructionsHope that this analysis will help you to be more focussed in your revision.
Do your best, let GOD do the rest.
Yours sincerely,
Mr Ng Song Seng
